Figured it out! The reason is that for spacelike intervals it is possible to choose a reference frame such that the two events x and y occur at the same time. This however is not possible for timelike ones.
Hi guys
So I am having trouble reparameterizing the geodesic equation in terms of coordinate time.
Normally you have:
\frac{d^2 x^{\alpha}}{d \tau^2} + \Gamma_{nm}^{\alpha} \frac{d x^{n}}{d \tau}\frac{d x^{m}}{d \tau} = 0
Where \tau is the proper time. I class we were told to express the...